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Math Help - Complex analysis help

  1. #1
    Junior Member
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    Complex analysis help

    Am doing some problems on complex analysis and am having some trouble getting my head around some of the basic points.

    If z represents a point R on the complex plane,

    and I take i . z to give another point T , then the line segment OT will be perpendicular to OR.

    to show this is true is the following correct?

    z = x +yi =  r.e^{(i.\theta)}

    and i.z = 1.e^{(i.(\pi/2))} . r.e^{(i.\theta)}

    therefore = r.e^{i(\theta + \pi/2)}
    and as the argument here has been shifted by pi/2 the second point is perpendicular from the first?
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  2. #2
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    That looks correct! However, don't forget that you can rotate by any multiple of 2 pi and still you will get the same answer.
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  3. #3
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    Cheers,

    Was unsure if the way i represented i was ok,
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